Kohn–Sham accuracy from orbital-free density functional theory via Δ-machine learning

Abstract

We present a Δ-machine learning model for obtaining Kohn–Sham accuracy from orbital-free density functional theory (DFT) calculations. In particular, we employ a machine-learned force field (MLFF) scheme based on the kernel method to capture the difference between Kohn–Sham and orbital-free DFT energies/forces. We implement this model in the context of on-the-fly molecular dynamics simulations and study its accuracy, performance, and sensitivity to parameters for representative systems. We find that the formalism not only improves the accuracy of Thomas–Fermi–von Weizsäcker orbital-free energies and forces by more than two orders of magnitude but is also more accurate than MLFFs based solely on Kohn–Sham DFT while being more efficient and less sensitive to model parameters. We apply the framework to study the structure of molten Al0.88Si0.12, the results suggesting no aggregation of Si atoms, in agreement with a previous Kohn–Sham study performed at an order of magnitude smaller length and time scales.

Overcoming the Chemical Complexity Bottleneck in on-the-Fly Machine Learned Molecular Dynamics Simulations

“…We previously adapted the on-the-fly ML algorithm developed by Jinnouchi et al and inspired by the Gaussian approximation potentials to correct orbital free DFT calculations to Kohn–Sham accuracy in the SPARC electronic structure code. , This implementation has been extended to be compatible with the full Kohn–Sham formalism with the option to use the SOAP or GMP descriptors with all on-the-fly functionality implemented in a development branch. The initial training set size and regularization strength for the ML models were systematically optimized using a grid search routine on the 6 element alloy and pure Pt.…”

“…The issue of unreliable uncertainty estimates is compounded by the dynamically updated threshold that is often used to overcome the lack of calibration in error estimates. , Once a large error is observed for a training point, the threshold increases, and the model is unable to recover because the DFT calculations are no longer triggered. This can be improved by using hueristics, such as periodically forcing DFT calculations, but this requires additional hyperparameters and can still lead to catastrophic failure between checks.…”